Does self-supervised learning require auxiliary tasks?
Most (if not all) self-supervised learning techniques for (visual or textual) representation learning use pre-text tasks, and many pre-text tasks have been proposed in recent years.
However, as I say in my other answer (which you cite), the term SSL has also been used (at least, in robotics: for example, see this paper, which I am very familiar with) to refer to techniques that automatically (although approximately) label the unlabelled dataset for your downstream task (i.e. image recognition), i.e. they automatically create a labeled dataset of pairs $(x_i, \hat{y}_i)$, where $x_i$ is an image that contains an object and $\hat{y}_i$ is the automatically (and possibly approximately) generated label (such as &quot;dog&quot;). This latter use of the term SSL is closer to some weakly supervised learning (WSL) techniques. Actually, it can be considered a WSL technique.
Now, in this specific paper, they actually solve some kind of pre-text task, i.e. they exploit the relations between two different sensors to produce the labels.
To answer your question more directly: in all SSL papers that I have come across, some kind of pre-text task is always solved, i.e., in some way, you need to automatically generate the supervisory signal, and that task that we solve with the automatically generated learning signal (with the purpose of learning representations or generating a labeled dataset) can be considered the pre-text task (which may coincide with the downstream task, for example, in the case you're training an auto-encoder with an unlabelled dataset for the purposes of image denoising).
In any case, I wouldn't bother too much about it. Just keep your context in mind when reading your paper. If you're really worried about it, then you should probably read almost all SSL-related papers, but, in that case, by the end of that, you will be an expert on the topic and you will not need our help (or my help).